1. Field of the Invention
The present invention relates to a second harmonic generator using a laser as a fundamental wave light source.
2. Description of the Prior Art
This type of second harmonic generator is adapted to reduce the wavelength of an output light from a light source into half for the purpose of reduction of the wavelength. Second harmonic generating elements (also termed as SHG elements) used in such a device are disclosed in E. J. Lim, et al, "Blue Light Generation by Frequency Doubling in Periodically Polled Lithium Niobate Channel Waveguide" Electronics Letters, Vol. 25, No. 11, pp. 731-732 (1989).
Referring to FIG. 1, which is a schematic perspective view of a second harmonic generating element, a concept of principle of operation, or quasi-phase matching method, of the SHG element, will be described. In this SHG element, a LiNbO.sub.3 substrate 10 has a +C surface in which Ti (titanium) has been thermally diffused periodically with the period of .LAMBDA. at the diffusion temperature of about 1,100.degree. C. for the diffusion time of about one hour to form a domain inversion structure 12, which is a grating-like structure. An optical waveguide 14 is formed by a proton exchange method (Li+--H+ exchange method) perpendicular to the domain inversion structure 12.
As shown in FIG. 1, a fundamental wave of an angular frequency of .omega. and a wavelength of .lambda.(.omega.) is introduced from the left in the optical waveguide 14 and propagates therein in an m-th propagation mode (m=0, 1, 2, . . . ) at an effective guide index of refractive index Nn (.omega.). As is well known, during this propagation a second harmonic of an angular frequency of 2.omega. and a wavelength .lambda.(2.omega.) is generated. In other words, a portion of energy of the fundamental wave .omega. is transferred to the second harmonic 2.omega..
Now, assuming that no domain inversion region has been formed, the amount of part of energy of the fundamental wave converted to the second harmonic becomes maximal when the fundamental wave propagates in the optical waveguide 14 by a length lc ( coherence length) given by the following formula: EQU lc=.lambda.(.omega.)/[4{Nn(2.omega.)-Nm(.omega.)}] (1)
wherein Nn(2.omega.) is the effective guide index for n-th propagation mode of the second harmonic, and Nm(.omega.) is the effective guide index for m-th propagation mode of the fundamental wave.
Hereafter, description will be made on a case where both the fundamental wave and the second harmonic propagate in zeroth (0-th) mode or fundamental modes, i.e., m=n=0, for simplicity. Here, coherence length lc depends on the fundamental wavelength .lambda.(.omega.) and the size of the optical waveguide. When .lambda.(.omega.)=860 nanometers (nm) and the thickness of the optical waveguide is on the order of d=1 micron, the amount lc is said to be on the order of 1.7 micron or micrometer (.mu.m). See Toshinori Nozawa, et al, "Optical-Device Applications of LiNbO.sub.3 Single Crystals" Oyo Butsur (Applied Physics, Japan), Vol. 59, No. 8, pp. 996-1013 (1990), Table 3). This value was obtained on the assumption that the deviation of the coherence length lc from a true value would not be so large if the coherence length lc is calculated from the fact that the guide index n(860) of a light having a wavelength of 0.860 micron from LiNbO.sub.3 is on the order of 2.1723 and the guide index n(430) of a light of a wavelength of 0.430 micron is on the order of 2.2987. See D. S. Smith, et al, "Refractive Indices of Lithium Niobate" Optics Communications, Vol. 17, No. 3, p. 332 (1976), using the value of n(860) as Nm(.omega.) and the value of n(430) as Nn(2.omega.).
The coherence length lc being 1.7 micron means that the intensity of the second harmonic becomes maximal as the fundamental wave propagates in the optical waveguide 14 by a length of 1.7 microns, and then becomes 0 (zero) as it propagates by a further length of 1.7 microns. In other words, the fact that the coherence length lc is finite rather than infinite indicates that phase matching between the fundamental wave and the second harmonic is incomplete, and that if the fundamental wave propagates in the optical waveguide 14 over a distance longer than the coherence length lc, the intensity of the second harmonic will not exceed a certain value.
The incomplete phase matching means a presence of phase mismatching. This phase mismatching .DELTA.k is given by the following formula: EQU .DELTA.k=(4.pi./.lambda.(.omega.))(N(2.omega.)-N(.omega.)).
Accordingly, as shown in FIG. 1, a domain inversion region 12 is provided for every coherence length lc to form a grating-like structure of domain inversion region 12 at a period of .LAMBDA.(=2 lc) so that phase mismatching .DELTA.k can be supplemented to enable outputting a second harmonic having an intensity proportional to substantially a second power of the distance in which the fundamental wave propagated.
The condition under which the phase mismatching is supplemented completely is given the following equation: EQU N(2.omega.)-N(.omega.)-.lambda.(2.omega.)/.LAMBDA.=0 (2)
See, Sasson Somekh, et al, "Phase Matching by Periodic Modulation of Nonlinear Optical Properties" Optics Communications, Vol. 6, No. 3, pp. 301-304 (1972), particularly formula (12) in the literature, for example.
Jonas Webjorn, et al, "Fabrication of Periodically Domain-Inverted Channel Waveguides in Lithium Niobate for Second Harmonic Generation" Journal of Lightwave Technology, Vol. 7, No. 10, pp. 1597-1600 (1989) recites this formula as it is. Even when a strict phase matching (N(2.omega.)-N(.omega.)-.lambda.(2.omega.)/.LAMBDA.=0) is not obtained, the formation of a periodical domain inversion structure which satisfies formula (2) makes it possible to take out a second harmonic (or SH light output) whose intensity is proportional to output or develop the second power of the distance of propagation of the fundamental wave, and thus of the length L of the SHG element.
However, the condition given by formula (2) is difficult to attain for the following two reasons: (1) Effective guide indices N(2.omega.) and N(.omega.) depend on the dimension of the optical waveguide used and the precision of dimension required here cannot be attained sufficiently with current state of technology; and
(2) The precision of dimension of period .LAMBDA. must be 1 nm or less but such precision of dimension cannot be attained sufficiently currently.
Then, use is made of a dye laser whose wavelength is variable for a light source for the fundamental wave in order to satisfy formula (2) so that conversion efficiency can be increased. See E. J. Lim et al, Electronics Letters, Vol. 25, No. 11, pp. 731-732 (1989).
However, the use of a dye laser for the light source for the fundamental wave leads to increased size of the overall second harmonic generator, and the second harmonic generator using a dye laser for the light source for the fundamental wave is of substantially no practical use because a monochromatic laser light is already available by gas laser or the like.